2 Answers
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There are a lot of ways to get this look. Instagram uses a predifined filter, but you can also do it "manually" in photoshop. Try for example:
->Filters -> Noise -> Dust and Scratches and you can play with the settings.

If you look at the "lint" you will see that it is the exact same texture in every photo.

The most common way to get this overlay to happen is to create a mask which is used to allow color in some areas and block out color in other areas. In the real world one might use a stencil and masking tape. In the digital world, it is achieved by using a special layer mask which contains a greyscale image (aka a black and white image).

While there are dust and scratch filters for this sort of thing, if you were sweep some dirt off the floor, sprinkle it onto a white piece of paper, then place the paper in direct sunlight and snap a close-up photo of it, you would have the basis for making a mask.

You would convert the color to greyscale, play with brightness and contrast, and paste it into the layer mask channel for a white layer.